Abstract
Since the introduction of spiral self-avoiding walks on the square lattice by Privman in 1983, there has been considerable interest in this model and its generalizations. Recent progress on various models of spiral self-avoiding walks and loops is reviewed. We discuss the methods to derive exact results for (I) the number Sn and the mean end-to-end distance Rn of spiral self-avoiding walks with n steps on the square and triangular lattices, (2) the number Cn of spiral self-avoiding loops with n steps on the square and triangular lattices, (3) the number of anisotropic spiral self-avoiding loops on the square lattice.
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